1. Field of the Invention
The present invention is directed to a method of distortion correction for gradient non-linearities in nuclear magnetic resonance tomography apparatus.
2. Description of the Prior Art
As is known, inhomogeneities in the basic magnetic field and non-linearities of gradient fields lead to image distortions if there are no corrective or preventative measures in the standard MR imaging sequences. Pulse sequences currently utilized are generally based on a technique referred to as the "Spin Warp" method as disclosed, for example, in U.S. Pat. No. 4,706,025. Each nuclear magnetic resonance signal is thereby phase-encoded in at least one direction before the readout and is frequency-encoded in another direction by a readout gradient during readout. A number of differently phase-encoded nuclear magnetic resonance signals are acquired. The nuclear magnetic resonance signals are sampled, digitized onto a grid in the k-space and entered into a raw data matrix in the k-space. A Fourier transformation in the phase-encoding direction as well as in the frequency-encoding direction is implemented in the raw data matrix for image acquisition.
A number of correction methods have been described in the literature wherein image distortions due to non-uniform magnetic fields are corrected by an after-processing (post-processing) of the raw data or of the calculated image data, for example, the article by J. Weis, L. Budinski, "Simulation of the Influence of Magnetic Field Inhomogeneity and Distortion Correction in MR Imaging" in Magnetic Resonance Imaging, Vol. 8, pp. 483-489, 1990. It is known from this reference to correct image distortions by after-processing of an image acquired in a conventional way (i.e. with at least two-dimensional Fourier transformation). The information about the magnetic field inhomogeneities that is thereby required, i.e. about the course of the basic magnetic field, is thereby acquired from the phase of separately registered spin echo images.
It is known from the article by C. -M. Lai, "Reconstructing NMR Images under Magnetic Fields with Large Inhomogeneities", in J. Phys. E: Sci. Instrum., Vol.15, 1982, pp.1093-1100, to involve inhomogeneities in the image reconstruction. This work is based on a technique that is no longer a standard projection reconstruction, whereby the known projection reconstruction algorithm is replaced by an algorithm wherein the previously identified magnetic field inhomogeneity is already taken into consideration in the image reconstruction.
If only inhomogeneities of the basic magnetic field are taken into consideration, these are relatively uncritical in the phase-encoding direction since the only concern is signal differences between the individual phase-encoding steps. In the direction of the readout gradient, however, the superimposition of the readout gradient with basic field inhomogeneities leads to distortions. In a method according to German OS 44 16 363, a conventional Fourier transformation is therefore implemented in the phase-encoding direction, whereas a generalized Fresnel transformation (wherein a previously identified location dependency of the basic magnetic field in readout direction is taken into account) is implemented in the readout direction.
If not only inhomogeneities of the basic magnetic field, but also non-linearities of the phase-encoding gradient are to be taken into consideration, then a correction must also be implemented in the phase-encoding direction. The outlay for the gradient coils can be reduced when a non-linear field course of the phase-encoding gradient is allowed in the examination field. A strong inducement to utilize non-linear gradients, or even a necessity to do so, exists in the case of the echo planar imaging (EPI) method. As is known, high-amplitude gradients must be switched extremely fast in EPI. This can lead to undesirable physiological stimulations of the patient, even pain in the extreme case. The problem is most serious at the edge of or at the outside the examination field since the largest gradient field swing occurs at those regions. This problem can thus be solved by causing the gradients to flatten toward the edge of the examination field, i.e., they are non-linear.